A bee is traveling at 5 MPH, and a train travelling in the opposite
direction at 100 MPH. The Bee collides with the train, now travelling
at the same speed as the train. Does the Bee at any point hit 0 MPH?

I suppose, on average, the answer is yes.

But what is happening in actuality is that the bee is disintergrating,
and different parts of its hapless body are moving at different
speeds, and even in totally different directions...the part of the bee
in first contact with the train has reversed direction while (for the
briefest instant) the rear of the bee is still moving forward.

Very vivid ...
Can any object reverse direction without for an instant having zero motion?

"Can any object reverse direction without for an instant having zero motion?"
No.

PS do your own homework gerbil, or you'll never be the one answering the questions.

Paf is quite correct. If you watch automobile crash video in slow
motion, you can see that areas of the car that has hit a stationary
object are still moving at quite a clip. In a 60 mph crash, the front
of the car is effectively motionless rather quickly while the back of
the car continues forward at ever reducing speed.

Same with the poor bee.

If we assume that the velocity of any part of the bee (or the average
of all its parts) is a continuous function, then by the intermediate
value theorem

http://mathworld.wolfram.com/IntermediateValueTheorem.html

it follow that the velocity must be zero at some point in time. If
time or space is discreet, perhaps the velocity it is not continuous,
but we have no useful theory of physics that predicts such a thing.

I must point out that the moment the train hits the bee, the bee stops beeing.

It then becomes a has-been.

For members of the non-scientific community, it is clearly a case of
seeing is beelieving.

Last thing to go through bee's mind after such an event?
His back-side!

Or, as I once read, a frequent remark on "black box" voice recorders is:
"Oh shit!"

yes yes gerbil, quote the intermediate value theorem as evidence, your
3rd grade prof will think you're brilliant =)

I've always thought  a frequent remark on "black box" voice recorders
is: Here, hold my beer, i'm going to try something different;)

Actually, and seriously, I suspect there is no guarantee that a bee
can hit a train moving at 100 mph.  The reason I say this is at that
speed there is a large cushion of air in front of the train and it may
well "blow" the bee aside rather than hit it. If of course depends
upon the shape of the train's front, and the weight of the bee, and
the exact point the bee approaches the train.

Tell that to all the bugs that commit harri-kirri on my car windscreen
when I take a trip. The "cushion of air" may slow down the impact, but
it certainly doesn't stop the inevitable splat! :-)

pafalafa has provided the real solution, but I saw this first as part of a paradox.
? for the bee to switch directions, it must stop at some point
? it seems reasonable that this occurs when it hits the train
? while the bee is on the train, they yare both moving at the same speed
? therefore: if the bee stopped, the train must have stopped also

the train ain't reversing directions mike, the bee is. a paradox it is not.

I love thought experiments.

The question can be phrased in a number of different ways. A
stationary bee is hovering, gets plastered by the high-speed train; is
the bee's speed ever below 100mph? Sure, that's one you can see. If it
is below 100mph, you can assume it might be zero at some point.
Instantaneous is a tough sell.

Replace the bee with a rubber ball and you can visualize the elastic
deformation and subsequent acceleration.

Now toss the ball at the moving train. Still see the deformation and
acceleration? Sure. Can the ball's speed ever be zero? Yep, but you
can start to see that some parts may be moving while other parts are
at zero speed.

Isn't this covered under "velocity" in physics?

Replace the rubber ball with a steel one and toss it at the train. A
bit harder to visualize, but still possible. Watch out for transit
cops.

Now replace the train with a Hupmobile. Replace the ball with a
turkey, which we used to call a "walking bird." Stand on your head.
Put your right foot in. Put your right foot out. Hah, I didn't say
"Simon Sez!"

Man, it's been a long day.

marcusl

i think you misread my comment: it was a tongue-in-cheek use of bad
logic and never suggested the train reversed direction

"Does the Bee at any point hit 0 MPH?"  NO

The train is ALWAYS moving at 100mph...hitting the bee does not effect
the train and therefore there will never be a point that the be is not
moving through space......

mikewa ha, my bad. =)

for you others, NO, the train is NOT always moving at 100mph. it slows
down, albeit very slightly.  momentum in the normal direction is
conserved, mass of the bee * initial velocity of bee + mass of the
train * initial velocity of the train = final mass bee *final velocity
bee + final mass train+final velocity train.

hackmonkey, you're totally incorrect. nothing can change directions instantaneously.

marcusl-ga, 

QUOTE

Nothing can change directions instantaneously.

UNQUOTE

You're totally incorrect!

A woman's mind.

(Haven't you seen them drive?)

They call it 'multitasking'.

Yes, for a very small time the bee stops, but the it is re-accelerated
in the other direction, what is very interesting is that if the bee
for an instant is doing 0 MPH the it follows that teh train for an
instant must also be traveling at 0 MPH, but this does not happen
because thh train slightely elasticly deforms, which allows the bee to
hit 0 MPH and the re-accelerate it in teh other direction.

I disagree with the above, Newton's laws of motion, and so on.

Going back to Pafalafa's comment, and forgetting for the moment that
the bee will disintergrate, I believe that the center of mass of a
less deformable object will stop for an instant, a small steel ball
for example.

Also if the bee is sliding along the front of the train for the
instant it takes to change direction then it never was going 0 mph due
to its movement along the front of the train, making kind of a
parabolic path.

I might not bee the best to ask, but the second the bee hit the train
wouldn't it already start beeing pushed in the opposite direction?
Almost skipping zero?